Question

Which of the following is the correct expanded form for the series below?

A. 1-1/2+1/4-1/8+1/16 B. 1-1/2-1/4-1/8-1/16 C. 0-1/2+1/4-1/8+1/16 D. 0-1/2-1/4-1/8-1/16

Answer 1

A. 1 -1/2 + 1/4 - 1/8 + 1/16

Explanation:

Answer 2

The correct answer is A. 1 -1/2 + 1/4 - 1/8 + 1/16

Explanation:

1. Let's review the information provided to us for solving the question:

Series ∑⁴n = 0 [ -1/2] ⁿ

2. Let's resolve the series:

For n = 0, (-1/2)⁰ = 1 (Any number raised to the power of zero, except zero, equals always to one)

For n = 1, (-1/2)¹ = -1/2

For n = 2, (-1/2)² = -1/2 * -1/2 = 1/4

For n = 3, (-1/2)³ = -1/2 * -1/2 * -1/2 = -1/8

For n = 4, (-1/2)⁴ = -1/2 * -1/2 * -1/2 * -1/2 = 1/16

The correct answer is A. 1 -1/2 + 1/4 - 1/8 + 1/16